My Panasonic tv displays only a thin blue horizontal line in the middle of the screen. It's an older analog tv (about 7 yrs old) not a flat screen. It was working fine when it was turned off; the next time it was turned on it displayed the blue line. Also, the set has a built in VCR which seems to be working fine (except the picture doesn't display - just the blue line.)

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Line faults & possible causes to LCD & Plasma screen are given with illustrations. You can get an idea about the fault to an extent. Faults to all LCD & Plasma screen are similar, irrespective of its brand and screen size.
Search the site by type in the "BRAND NAME" of your device; (Exclude the model number), in the "Search box at the top right of the display window of the Homepage" to get gathered related posts

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Details about how to repair this fault is there.
Type in " My service table today " as search phrase; in its search box at the top right of the display window, to get gathered related pages together. It will make search easy.

If you wish to get some details; check the site linked here. Pull up older posts. Surf the site with patience. http://electronicshelponline.blogspot.com/
Line, faults & possible causes to both LCD & Plasma TV screen are given with illustrations. You can get an idea about the fault to an extent.

are the lines going left to right or up or down? if up or down probaly a bad panel,iff left or right either the upper or lower buffer board is bad

Sound like your Y-Sustain board has one foot in the grave. The Y upper buffer and Y lower buffer boards go when the Y Sus Goes too...

Nothing you can do about that...get used to it or change the TV.
It's a defect in the panel that can't be reliably fixed.

problem could also be inside the display panel.

Sounds like a faulty Plasma Display Panel.

Contact Panasonic and find out if it is still covered under warranty.

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Amardeep
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The line is there because the vertical deflection unit - the one that spreads that line across the entire screen to form the image - has failed. Replacing it is a job for a professional, or at least an experienced amateur, and the parts will be quite difficult to find for such an old tv . 

The vertical deflection has gone out. Put it in the shop.